Function generator



April 10, 1956 A. F. FAIRBANKS FUNCTION GENERATOR 2 Sheets-Sheet 1 Filed Oct. 16. 1951 FIG.!

FIG. 2

AVARD F. FAIRBANKS FIG. 3

ATTORNEY April 10, 1956 A. F. FAIRBANKS FUNCTION GENERATOR 2 Sheels Sheet 2 Filed Oct. 16, 1951 H IIIIY FIG. 4

I N V EN TOR.

AVARD E FAIRBANKS Mu /w FIG.

ATTORNEY United states ifatent 2,741,140 Patented Apr. 10, 1956 rUNcrioN GENERATOR Avard F. Fairbanks, Garvey, Calif, assignor to North American Aviation, inc.

Application October 16, 1951, Serial No. 251,616

11 Claims. (Cl. 74-4245) This invention relates to the generation of a predetermined mathematical function, and particularly to a mechanical device for producing a shaft rotation which is a predetermined function of a second shaft rotation.

In the design of computers it is often necessary to produce a shaft rotation which is a precise, predetermined function of another shaft rotation. In the past it has been customary to utilize cams and cam followers or gear cams to achieve this result. One difficulty attendant with the use of these conventional devices is that the output shaft rotation is limited in range and speed. A further difiiculty is that cams or gearcams are difficult to fabricate. It is therefore an object of this invention to provide means for producing a shaft rotation which is a predetermined function of another shaft rotation.

It is another object of this invention to provide a mechanical function generator which is capable of generating a function which passes through a zero point.

It is another object of this invention to provide means for producing simultaneously a plurality of shaft rotations, each of which is a different predetermined function of a given shaft rotation.

It is another object of this invention to provide a function generator which is capable of reversing.

it is another object of this invention to provide a function generator which is easy to reproduce.

Other objects of invention will become apparent from the following description taken in connection with the accompanying drawings, in which:

Fig. 1 is a plan view of the invention;

Fig. 2 is a sectional view of the invention taken at 2-2 in Fig. 1;

Fig. 3 is a drawing illustrating the method of making the master disc for the function generator of this invention;

Fig. 4 is a side elevation partly in section showing moulding of the disc of the function generator of this invention;

Fig. 5 is a plan view of a second embodiment of the invention;

And Fig. 6 is an elevational view of the device shown in Fig. 5.

Referring now to Figs. 1 and 2, there is shown a cylindrical disc 1 having pins 2 and supported for roration upon a shaft 3. Shaft 3 carries gear 4 which engages gear 5 driven by shaft 6 which is connected .to be driven by a motor 7. Shaft 6 also drives gear 8 which in turn drives gear 9. Gear 9 is attached to threaded shaft 16 which is rotatably supported by frame members 11 and 12. Frame members 11 and 12 also rotatably support keyed shaft 13 upon which is carried pin gear 14 so that gear 14 is free to slide axially upon shaft 13 but is not free to rotate-except with shaft 13. Lead nut 15 is carded upon the threads of shaft 10 and is advanced by the rotation of shaft 10, carrying with it gear 14.

It is desirable that the spacing between pins rather than the pitch of the spiral indicate the function to be generated. Therefore, pins 2 are arranged upon disc 1 in a uniformly pitched spiral pattern and with a spacing between pins which is dependent upon the function to be generated. As motor 7 rotates shaft 6, shaft 19 is turned through gears 5, 8, and 9, and lead nut 15 is caused to scan disc 1. Of course, as motor 7 turns, disc 1 also turns so that pin gear 14 is caused to engage successive pins upon disc 1. As these successive pins are engaged, the pin gear is turned a fifth of a revolution each time a pin is engaged. Shaft 13, which is the output shaft, is also turned, since pin gear 14 is keyed thereto. The result, therefore, is that if motor 7 is turned through an angle 0, output shaft 13 is turned through an angle equal to some function of 0 as determined by the spacing of pins 2 upon disc 1.

Pins 2 are variably spaced, that is, they may be spaced as close as permitted by the spacing of the teeth on pin gear 14, and as far apart as is necessary to describe the function required to be generated. The device shown in Figs. 1 and 2 is particularly advantageous Where a large number of identical function generators must be provided, because the function discs with their pins may be produced readily by means of apparatus shown in Figs. 3 and 4.

Referring to Fig. 3, a disc 16 is carried upon a rotatable vertical shaft 17 which is rotated by means of gears 18 and 19, and shaft 20 attached to gear 21 driven by gear 22 which in turn is rotated by hand crank 23. Gear 22 is also attached to a Worm 24 which is adapted to advance frame 25 to which is attached drill 26. Drill 26 is free to slide upon bar 27. As worm 24 rotates, it drives a counter 28 by means of gears 29 and 30. In operation, the hand crank is turned until counter 28 reads some predetermined number. The drill motor is then used to drill a conical hole in disc 16. A prepared table of equal increments of the output function vs. disc rotation in terms of counter readings may conveniently be utilized. As each counter reading is achieved the drill is depressed by compression of spring 31 and the function is generated along a spiral path, since at each turn of the hand crank the drill is advanced diametrally along the disc. As soon as all the conical holes are cut in disc 16, disc 16 is used as a master by pouring molten metal or plastic upon the surface thereof to achieve a molded function generator disc similar to that shown as disc 1 in Figs. 1 and 2.

Referring to Fig. 4, master disc 16 with stub shaft 33 is shown after molten plastic, metal, or other material has been poured into it to achieve a disc such as disc 1 of Figs. 1 and 2. It will be noted that disc 1 then has the pins that are required to describe the function to be generated when the disc is used in connection with the apparatus shown in Fig. 1.

Referring now to Fig. 5, there is shown a second embodiment of the invention which is adapted to turn the output shaft in either direction. in Fig. 5 a disc 34 having peripheral gear teeth 35 is driven by a worm 36 which in turn is driven by input shaft 37 through gears 38 and 39 and shaft 41). Input shaft 37 also drives gears 41 and 42 which in turn are connected to drive lead screw 43. Lead screw 43 has right-hand threads on its left-hand half and left-hand threads on its right-hand half as shown in Fig. 5. Lead screw 43 is supported by bearing members 44 and 45 and is free to rotate with respect to block 46. Nuts 47 and 48 are threaded to the two halves of lead screw 43 so that when lead screw 43 is rotated, nuts 47 and 48 translate either toward or away from the center of disc 34. Nuts 47 and 48 slide upon keyed shaft 49 as do pin gears 50 and 51. Pin gears 50 and 51 cause keyed shaft 49 to turn, but shaft 49 does not cause nuts 47 and 4510 turn. Pins 52 in 'disc 34 are arranged in parallel spiral patterns which are synchronized with the motion of nuts 47 and 48 upon lead screw 43 so that pin gears 59 and 51 follow different spiral rows of pins on disc 34. If pins 52 are so spaced that when one of them engages pin gear 50 no pins are engaging pin gear 51, output shaft 49 may be caused to rotate first in one direction and then in the other. This permits the device to describe a function which passes through a zero point and goes from positive to negative and negative to positive in terms of the output shaft rotation. Thus, if a certain input shaft rotation is supplied to input shaft 37, any predetermined function may be described by the output shaft 49, since it may be caused to rotate first in'one direction and then in the other.

Referring now to Fig. 6, there is "shown a third embodiment of the invention which is only a slight modification-of the device shown in Fig. 5. In Fig. 6 'a doublcsided disc 53, having pins on both sides thereof is rotated with the identical mechanism shown in'Fig. 5. The same output is achieved by means of 'pin gears '50 and '51 at the top of the disc as *is achieved in "Fig. 5. However, on the lower side of the disc there is provided means for achieving a directional output which .is vnonrevers'ing. In Fig. 6, output shaft '54 will be rotated in one direction and output shaft 55 will be rotated in the opposite direction and in accordance with the functions set by the positions of the pins in their respective spirals. Pin gears 56 and 57 drive output shafts 54 and 55, respec'tiveiy, in the-same manner as do pin gears 50 and-51 s'hown'in Fig. 5. With a single disc, then, it is possible to achieve three different functions of a single input merely by use of .a disc having pins on both sidesthereof.

Although the invention has been described and illustrated in detail, it is to be clearly understood that the same is by way of illustration and example only and is no't'to be taken by way of limitation, the spirit and scope of this invention being limited only by the terms of the appended claims.

I claim:

1. Means for producing a shaft rotation which is a predetermined function of another shaft rotation comprising a disc having a plurality of pins arranged in a uniformly pitched spiral path on one side thereof, said pins -being spaced apart according to a predetermined varying function, an output shaft disposed adjacent said disc, a pin gear slideable upon said shaft and connected to turn said shaft when it engages pins upon said disc, and means for causing said pin gear to scan said disc as said disc is rotated so as to follow the spiral path of said pins on said disc whereby said output shaft rotation is a predeterminedfunction of the rotation of said disc.

'2. .A device as recited .in claim 1 in which said means for causing said pin gear to scan comprises a lead screw drivcably connected to said disc for moving said pin gear along a diameter of said disc.

3. 'Means for producing an output shaft rotation proportional to a predetermined, varying function of an input shaft rotation comprising a disc, .aplurality of pins projectingfrom one face of said disc and variably spaced in accordance with said function in a continuous, uniformly pitchedspiral row, a pin gear adapted to engage said .pins andto be rotated thereby when said disc is rotated, means for coordinating the motion of said'pin gear along a diameter of said disc so that it follows said spiral row, and means for causing said output shaft to rotate with said pin gear v-to'thereby generate as an outputshaftrotation a predetermined function of the rotation of said disc.

4. A function generator comprising a cylindrical ldisc, means for rotating said disc in accordance with some predetermined shaft rotation, an output shaft disposed adjacent one face of said disc, two pin gears opposed with respect to each other, upon :the face :of said disc, and slideable upon said output .s'haft but restrained to rotate therewith, a plurality of pins upon said disc,

said pins being variably spaced in parallel spiral paths of' uniform pitch and adapted to engage said pin gears, and means for causing said pin gears to follow said spiral paths when said disc is rotated whereby said output shaft may be caused to described a function of the rotation of said disc, which function passes through zero.

5. A device as recited in claim 4 and further comprising a second output shaft arranged on the opposite side of said disc from said first outputshaft, a third pin gear upon said output shaft, a third output shaftarranged coaxially with said second output shaft, a fourth pin gear on said third output shaft, a plurality of pins arranged in uniformly pitchedspiral paths with predeterminedspacing between pins upon the side of said disc adjacent said third and fourth pin gears and means for causing said pin gears to follow said rows of pins on said disc as said disc is rotated whereby said three output shafts described three different functions of the rotation of said disc.

6. A function generator for producing ,a rotation of an output shaft which is a predetermined function of .an input shaft rotation comprising a cylindrical disc driveably connected to said input shaft and having a plurality ofprotrusions on one surface thereof arranged in a ,continuous, uniformly pitched spiral row with predetermined varied spacing between protrusions, and means for rotating said output shaft by an amount inversely proportional to the spacing of said protrusions to thereby rotate said output shaft according to a predetermined function of the rotation of said input shaft.

7. A device as recited in claim 6 in which said means for rotating said output shaft comprises a pin gear keyed to said shaft and disposed to engage said protrusions and means for moving said pin gear along said shaft in coordination with the rotation of said disc to cause said pin gear to follow the spiral row of said protrusions to thereby turn said output shaft according to a predetermined function of the rotation of said input shaft.

8. A function generator comprising a cylindrical disc, means for rotating said disc in accordance With-some predetermined function, a first output shaft disposed adjacent one face of said disc upon an axis parallel to .adiameter thereof, a second output shaft disposed parallel to said first output shaft and extending adjacent one-half of said disc on the opposite side of said disc from said .first outputshaft, a third output shaft coaxial with said .second outputshaft and extending adjacent the other half of said disc, a pair of pin gears .slideable on said first output shaft and driveably connected thereto, a pin gear slidcable on said second output shaft, apin gear slideable onsaid third output shaft, a pair of uniformly pitched spiral :rows, of predeterminately spaced pins on the side of said disc jadjacent {said first output shaft, the pins in each row arranged to engage teeth of one of said pair of pin gears nonsimultaueously withthe otherof said pin gears, a uniformly pitched spiral row of predetermiuately spaced pins on said disc arranged to engage the pin gear on said second outputshaft, :a uniformly pitched spiral row of predeterminately spaced pins on said disc arranged to engage the pingearon said third output shaft, and means for changing the radial coordinate of said pin gears with respect to saiddisc 'tofollow said spiral rows whereby said output shafts may be caused to describe three differentfunctions of the-rotation of said disc. I

.9. .A function generator comprising ,a rotatable disc, a plurality of variably spaced protrusions arranged in a spiral new of uniform pitch :upon said rotatable disc, a gear adapted to engage said protrusions, "and means for causing said gear to follow said spiral row of protrusions.

ll). .A function generator comprising a rotatable disc, a plurality of variably spaced protrusions arranged in a spiral row of uniform pitch upon the face of said rotatable disc, [an output shaft disposed adjacent said disc, a gear axially islideable upon said shaft, restrained to rotate therewith, and adapted to engage said protrusions, a lead-screw adapted to rotate :in accordance with the rotation of said disc, and a nut upon said lead screw adapted to drive said gear along said output shaft and cause said gear to follow said spiral row of protrusions.

11. A function generator comprising a disc having a plurality of protrusions on one surface thereof arranged in two uniformly pitched spiral rows with predetermined varied spacings between protrusions, an output shaft diametrically disposed adjacent one face of said disc, two pin gears each longitudinally slidable upon said output shaft and restrained to rotate therewith, said pin gears adapted to be rotated by said protrusions, means for said pin gears to spirally scan said disc by sliding longitudinally along said output shaft comprising a pair of nuts adapted to drive said pin gears longitudinally along said output shaft, and a lead screw rotated in accordance with the rotation of said disc and adapted to engage and drive said nuts simultaneously in opposite directions.

References Cited in the file of this patent UNITED STATES PATENTS 2,295,997 Mason et al. Sept. 15, 1942 2,295,998 Maxson et al. Sept. 15, 1942 2,329,683 Vaughn Sept. 14, 1943 2,405,473 Valentine Aug. 6, 1946 FOREIGN PATENTS 618 Great Britain Jan. 9, 1914 

